We investigate the thermodynamical properties of charged torus-like black holes and take it as the working substance to study the heat engines. In the extended phase space, by interpreting the cosmological constant as the thermodynamic pressure, we derive the thermodynamical quantities by the first law of black hole thermodynamics and obtain the equation of state. Then, we calculate the efficiency of the heat engine in the Carnot cycle as well as the rectangular cycle, and investigate how the efficiency changes with respect to volume. In addition, to avoid a negative temperature, we emphasize that the charge of this black hole cannot be arbitrary. Last, we check the calculation accuracy of a benchmark scheme and discuss the upper bound and lower bound for charged torus-like black hole in the scheme.

我们研究带电的圆环状黑洞的热力学性质，并将其作为研究热机的工作物质。在扩展相空间中，通过将宇宙常数解释为热力学压力，我们根据黑洞热力学的第一定律推导了热力学量，并获得了状态方程。然后，我们计算卡诺循环和矩形循环中热机的效率，并研究效率如何随体积变化。另外，为避免产生负温度，我们强调该黑洞的电荷不能是任意的。最后，我们检查基准方案的计算准确性，并讨论方案中带电圆环状黑洞的上限和下限。